Implementing Geometric Complexity Theory: On the Separation of Orbit Closures via Symmetries

Understanding the difference between group orbits and their closures is a key difficulty in geometric complexity theory (GCT): While the GCT program is set up to separate certain orbit closures, many beautiful mathematical properties are only known for the group orbits, in particular close relations with symmetry groups and invariant spaces, while the orbit closures seem much more difficult to understand. However, in order to prove lower bounds in algebraic complexity theory, considering group orbits is not enough. In this paper we tighten the relationship between the orbit of the power sum polynomial and its closure, so that we can separate this orbit closure from the orbit closure of the product of variables by just considering the symmetry groups of both polynomials and their representation theoretic decomposition coefficients. In a natural way our construction yields a multiplicity obstruction that is neither an occurrence obstruction, nor a so-called vanishing ideal occurrence obstruction. All multiplicity obstructions so far have been of one of these two types. Our paper is the first implementation of the ambitious approach that was originally suggested in the first papers on geometric complexity theory by Mulmuley and Sohoni (SIAM J Comput 2001, 2008): Before our paper, all existence proofs of obstructions only took into account the symmetry group of one of the two polynomials (or tensors) that were to be separated. In our paper the multiplicity obstruction is obtained by comparing the representation theoretic decomposition coefficients of both symmetry groups. Our proof uses a semi-explicit description of the coordinate ring of the orbit closure of the power sum polynomial in terms of Young tableaux, which enables its comparison to the coordinate ring of the orbit.Comment: 47 page

Ornithine transcarbamylase deficiency

Course Code: Biochemistry 5614Biochemistr

The PTF Orion Project: a Possible Planet Transiting a T-Tauri Star

We report observations of a possible young transiting planet orbiting a previously known weak-lined T-Tauri star in the 7-10 Myr old Orion-OB1a/25-Ori region. The candidate was found as part of the Palomar Transient Factory (PTF) Orion project. It has a photometric transit period of 0.448413 +- 0.000040 days, and appears in both 2009 and 2010 PTF data. Follow-up low-precision radial velocity (RV) observations and adaptive optics imaging suggest that the star is not an eclipsing binary, and that it is unlikely that a background source is blended with the target and mimicking the observed transit. RV observations with the Hobby-Eberly and Keck telescopes yield an RV that has the same period as the photometric event, but is offset in phase from the transit center by approximately -0.22 periods. The amplitude (half range) of the RV variations is 2.4 km/s and is comparable with the expected RV amplitude that stellar spots could induce. The RV curve is likely dominated by stellar spot modulation and provides an upper limit to the projected companion mass of M_p sin i_orb < 4.8 +- 1.2 M_Jup; when combined with the orbital inclination, i orb, of the candidate planet from modeling of the transit light curve, we find an upper limit on the mass of the planetary candidate of M_p < 5.5 +- 1.4 M_Jup. This limit implies that the planet is orbiting close to, if not inside, its Roche limiting orbital radius, so that it may be undergoing active mass loss and evaporation.Comment: Corrected typos, minor clarifications; minor updates/corrections to affiliations and bibliography. 35 pages, 10 figures, 3 tables. Accepted to Ap

TOI-561 b: A Low Density Ultra-Short Period "Rocky" Planet around a Metal-Poor Star

TOI-561 is a galactic thick disk star hosting an ultra-short period (0.45 day orbit) planet with a radius of 1.37 R$_{\oplus}$, making it one of the most metal-poor ([Fe/H] = -0.41) and oldest ($\sim$10 Gyr) sites where an Earth-sized planet has been found. We present new simultaneous radial velocity measurements (RVs) from Gemini-N/MAROON-X and Keck/HIRES, which we combined with literature RVs to derive a mass of M$_{b}$=2.24 $\pm$ 0.20 M$_{\oplus}$. We also used two new Sectors of TESS photometry to improve the radius determination, finding R$_{b}$=$1.37 \pm 0.04 R_\oplus$, and confirming that TOI-561 b is one of the lowest-density super-Earths measured to date ($\rho_b$= 4.8 $\pm$ 0.5 g/cm$^{3}$). This density is consistent with an iron-poor rocky composition reflective of the host star's iron and rock-building element abundances; however, it is also consistent with a low-density planet with a volatile envelope. The equilibrium temperature of the planet ($\sim$2300 K) suggests that this envelope would likely be composed of high mean molecular weight species, such as water vapor, carbon dioxide, or silicate vapor, and is likely not primordial. We also demonstrate that the composition determination is sensitive to the choice of stellar parameters, and that further measurements are needed to determine if TOI-561 b is a bare rocky planet, a rocky planet with an optically thin atmosphere, or a rare example of a non-primordial envelope on a planet with a radius smaller than 1.5 R$_{\oplus}$.Comment: Accepted to AJ on 11/28/202

Developing priority variables ("ecosystem Essential Ocean Variables" — eEOVs) for observing dynamics and change in Southern Ocean ecosystems

Reliable statements about variability and change in marine ecosystems and their underlying causes are needed to report on their status and to guide management. Here we use the Framework on Ocean Observing (FOO) to begin developing ecosystem Essential Ocean Variables (eEOVs) for the Southern Ocean Observing System (SOOS). An eEOV is a defined biological or ecological quantity, which is derived from field observations, and which contributes significantly to assessments of Southern Ocean ecosystems. Here, assessments are concerned with estimating status and trends in ecosystem properties, attribution of trends to causes, and predicting future trajectories. eEOVs should be feasible to collect at appropriate spatial and temporal scales and are useful to the extent that they contribute to direct estimation of trends and/or attribution, and/or development of ecological (statistical or simulation) models to support assessments. In this paper we outline the rationale, including establishing a set of criteria, for selecting eEOVs for the SOOS and develop a list of candidate eEOVs for further evaluation. Other than habitat variables, nine types of eEOVs for Southern Ocean taxa are identified within three classes: state (magnitude, genetic/species, size spectrum), predator–prey (diet, foraging range), and autecology (phenology, reproductive rate, individual growth rate, detritus). Most candidates for the suite of Southern Ocean taxa relate to state or diet. Candidate autecological eEOVs have not been developed other than for marine mammals and birds. We consider some of the spatial and temporal issues that will influence the adoption and use of eEOVs in an observing system in the Southern Ocean, noting that existing operations and platforms potentially provide coverage of the four main sectors of the region — the East and West Pacific, Atlantic and Indian. Lastly, we discuss the importance of simulation modelling in helping with the design of the observing system in the long term. Regional boundary: south of 30°S

Pan-Cancer Analysis of lncRNA Regulation Supports Their Targeting of Cancer Genes in Each Tumor Context

Long noncoding RNAs (lncRNAs) are commonly dys-regulated in tumors, but only a handful are known toplay pathophysiological roles in cancer. We inferredlncRNAs that dysregulate cancer pathways, onco-genes, and tumor suppressors (cancer genes) bymodeling their effects on the activity of transcriptionfactors, RNA-binding proteins, and microRNAs in5,185 TCGA tumors and 1,019 ENCODE assays.Our predictions included hundreds of candidateonco- and tumor-suppressor lncRNAs (cancerlncRNAs) whose somatic alterations account for thedysregulation of dozens of cancer genes and path-ways in each of 14 tumor contexts. To demonstrateproof of concept, we showed that perturbations tar-geting OIP5-AS1 (an inferred tumor suppressor) andTUG1 and WT1-AS (inferred onco-lncRNAs) dysre-gulated cancer genes and altered proliferation ofbreast and gynecologic cancer cells. Our analysis in-dicates that, although most lncRNAs are dysregu-lated in a tumor-specific manner, some, includingOIP5-AS1, TUG1, NEAT1, MEG3, and TSIX, synergis-tically dysregulate cancer pathways in multiple tumorcontexts

Pan-cancer Alterations of the MYC Oncogene and Its Proximal Network across the Cancer Genome Atlas

Although theMYConcogene has been implicated incancer, a systematic assessment of alterations ofMYC, related transcription factors, and co-regulatoryproteins, forming the proximal MYC network (PMN),across human cancers is lacking. Using computa-tional approaches, we define genomic and proteo-mic features associated with MYC and the PMNacross the 33 cancers of The Cancer Genome Atlas.Pan-cancer, 28% of all samples had at least one ofthe MYC paralogs amplified. In contrast, the MYCantagonists MGA and MNT were the most frequentlymutated or deleted members, proposing a roleas tumor suppressors.MYCalterations were mutu-ally exclusive withPIK3CA,PTEN,APC,orBRAFalterations, suggesting that MYC is a distinct onco-genic driver. Expression analysis revealed MYC-associated pathways in tumor subtypes, such asimmune response and growth factor signaling; chro-matin, translation, and DNA replication/repair wereconserved pan-cancer. This analysis reveals insightsinto MYC biology and is a reference for biomarkersand therapeutics for cancers with alterations ofMYC or the PMN

Genomic, Pathway Network, and Immunologic Features Distinguishing Squamous Carcinomas

This integrated, multiplatform PanCancer Atlas study co-mapped and identified distinguishing molecular features of squamous cell carcinomas (SCCs) from five sites associated with smokin

Spatial Organization and Molecular Correlation of Tumor-Infiltrating Lymphocytes Using Deep Learning on Pathology Images

Beyond sample curation and basic pathologic characterization, the digitized H&E-stained images of TCGA samples remain underutilized. To highlight this resource, we present mappings of tumorinfiltrating lymphocytes (TILs) based on H&E images from 13 TCGA tumor types. These TIL maps are derived through computational staining using a convolutional neural network trained to classify patches of images. Affinity propagation revealed local spatial structure in TIL patterns and correlation with overall survival. TIL map structural patterns were grouped using standard histopathological parameters. These patterns are enriched in particular T cell subpopulations derived from molecular measures. TIL densities and spatial structure were differentially enriched among tumor types, immune subtypes, and tumor molecular subtypes, implying that spatial infiltrate state could reflect particular tumor cell aberration states. Obtaining spatial lymphocytic patterns linked to the rich genomic characterization of TCGA samples demonstrates one use for the TCGA image archives with insights into the tumor-immune microenvironment

Public Versus Private: Does It Matter for Water Conservation? Insights from California

This article asks three connected questions: First, does the public view private and public utilities differently, and if so, does this affect attitudes to conservation? Second, do public and private utilities differ in their approaches to conservation? Finally, do differences in the approaches of the utilities, if any, relate to differences in public attitudes? We survey public attitudes in California toward (hypothetical but plausible) voluntary and mandated water conservation, as well as to price increases, during a recent period of shortage. We do this by interviewing households in three pairs of adjacent public and private utilities. We also survey managers of public and private urban water utilities to see if they differ in their approaches to conservation and to their customers. On the user side we do not find pronounced differences, though a minority of customers in all private companies would be more willing to conserve or pay higher prices under a public operator. No respondent in public utility said the reverse. Negative attitudes toward private operators were most pronounced in the pair marked by a controversial recent privatization and a price hike. Nonetheless, we find that California’s history of recurrent droughts and the visible role of the state in water supply and drought management undermine the distinction between public and private. Private utilities themselves work to underplay the distinction by stressing the collective ownership of the water source and the collective value of conservation. Overall, California’s public utilities appear more proactive and target-oriented in asking their customers to conserve than their private counterparts and the state continues to be important in legitimating and guiding conservation behavior, whether the utility is in public hands or private